{"id":45226,"date":"2023-06-27T16:59:57","date_gmt":"2023-06-27T16:59:57","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=45226"},"modified":"2026-03-30T19:34:26","modified_gmt":"2026-03-30T19:34:26","slug":"other-return-measures","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/other-return-measures\/","title":{"rendered":"Other Return Measures"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Rates and Returns (2025 CFA\u00ae Level I Exam \u2013 Quantitative Methods \u2013 Module 1)\",\n  \"description\": \"CFA\u00ae Level I Quantitative Methods video lesson by AnalystPrep covering Rates and Returns (Module 1). Professor James explains the required rate of return and discount rate, opportunity cost and the risk-free rate, arithmetic versus geometric returns, money-weighted and time-weighted returns, and continuously compounded and annualized returns. These core concepts form the foundation for CFA Level I exam preparation and support more advanced topics in Levels II and III.\",\n  \"uploadDate\": \"2024-02-21T00:00:00+00:00\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/QIl6JH_PuW8\/default.jpg\",\n  \"contentUrl\": \"https:\/\/www.youtube.com\/watch?v=QIl6JH_PuW8\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/QIl6JH_PuW8\",\n  \"duration\": \"PT1H57S\"\n}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"A $7,500,000 equity portfolio is 35% financed by debt at a cost of 5% per annum. If the equity portfolio generates a 9% annual total investment return, the leverage return is closest to:\",\n    \"text\": \"A $7,500,000 equity portfolio is 35% financed by debt at a cost of 5% per annum. If the equity portfolio generates a 9% annual total investment return, the leverage return is closest to:\",\n    \"answerCount\": 3,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"8.25%.\"\n    },\n    \"suggestedAnswer\": [\n      {\n        \"@type\": \"Answer\",\n        \"text\": \"11.15%.\"\n      },\n      {\n        \"@type\": \"Answer\",\n        \"text\": \"14.00%.\"\n      }\n    ]\n  }\n}\n<\/script>\n\n\n\n<p>\n  <iframe loading=\"lazy\"\n    src=\"\/\/www.youtube.com\/embed\/QIl6JH_PuW8\"\n    width=\"611\"\n    height=\"343\"\n    allowfullscreen=\"allowfullscreen\">\n  <\/iframe>\n<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Other Return Measures<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Gross and Net Return<\/h3>\n\n\n\n<p>The gross return is what an asset manager earns before subtracting various costs such as management fees, custody fees, taxes, and other administrative expenses. However, it does account for trading costs such as commissions.<\/p>\n\n\n\n<p>Gross return does not consider management or administrative costs. For this reason, it is a suitable metric for assessing and comparing the investment expertise of asset managers.<\/p>\n\n\n\n<p><strong>Net return<\/strong> is a metric for how much an&nbsp;investment has earned for the investor. It considers all administrative and management costs that reduce an investor\u2019s return.<\/p>\n\n\n\n<div style=\"text-align: center; margin: 24px 0;\">\n  <div style=\"max-width: 680px; margin: 0 auto;\">\n    <a href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"\n       style=\"display: inline-flex; align-items: center; justify-content: center;\n       width: 100%; padding: 12px 20px;\n       border: 2px solid #1a73e8; border-radius: 999px;\n       color: #1a73e8; text-decoration: none;\n       font-size: 15px; font-weight: 600;\n       line-height: 1.2; white-space: nowrap;\">\n      Practice return measures and performance analysis through our free trial.\n    <\/a>\n  <\/div>\n<\/div>\n\n\n<h3>Pre-tax and After-tax Nominal Return<\/h3>\n<p>Unless otherwise stated, all returns are nominal pre-tax returns in general. Depending on the jurisdiction, different rates apply to capital gains and income. Long-term and short-term taxes may also be applied to capital gains.<\/p>\n<p>The after-tax nominal return is determined by subtracting any tax deductions applied to dividends, interest, and realized gains from the total return.<\/p>\n<h3>Real Returns<\/h3>\n<p>Returns are typically presented in nominal terms, which consist of three components: the real risk-free return as compensation for postponing consumption, inflation as compensation for the loss of purchasing power, and a risk premium. Real returns are useful in comparing returns over different periods, given that inflation rates vary over time.<\/p>\n<p>Recall the relationship between the nominal rate and the real rate:<\/p>\n<p>$$\\text{(1+ Nominal Risk-free rate)=(1+Real risk free rate)(1+Inflation premium)}$$<\/p>\n<p>We can find the connection between nominal and real returns by considering the real risk-free rate of return and the inflation premium. This relationship can be expressed as:<\/p>\n<p>$$(1+\\text{Real Return})=\\frac{(1+\\text{Real risk-free rate})(1+\\text{Risk premium})}{1+\\text{Inflation premium}}$$<\/p>\n<p>Real returns become particularly useful when you want to compare returns across various time periods and different countries. This is especially important when returns are shown in local currencies and when inflation rates vary from one country to another.<\/p>\n<p>After-tax real return is the amount the investor receives as payment for delaying consumption and taking on risk after paying taxes on investment.<\/p>\n<h3>Leveraged Returns<\/h3>\n<p>If an investor uses derivative instruments within a portfolio or borrows money to invest, then leverage is introduced into the portfolio. The leverage amplifies the returns on the investor&#8217;s capital, both upwards and downwards.<\/p>\n<p>The leveraged return considers the actual return on the investment and the cost\u00a0of the borrowed money. The cost of borrowing and financing fees are\u00a0subtracted from the overall return produced by the investment to determine the leveraged return.<\/p>\n<p>Using the borrowed capital (debt) increases the size of the leveraged position by the additional borrowed capital.<\/p>\n<p>Intuitively, the leveraged return is given by:<\/p>\n<p>$$\\begin{align}R_L&amp;=\\frac{\\text{Portfolio return}}{\\text{Portfolio equity}}\\\\&amp;=\\frac{\\left[R_P\\times\\left(V_E+V_B\\right)-(V_B\\times r_D)\\right]}{V_E}\\\\&amp;=R_P+\\frac{V_B}{V_E}\\left(R_P-r_D\\right)\\end{align}$$<\/p>\n<p>Where:<\/p>\n<p>\\(R_L\\) = Return earned on the leveraged portfolio.<\/p>\n<p>\\(R_P\\) = Total investment return earned on the leveraged portfolio.<\/p>\n<p>\\(V_B\\) = Value of debt in the portfolio.<\/p>\n<p>\\(V_E\\) = Value of equity in the portfolio.<\/p>\n<p>\\(r_D\\) = Borrowing cost on debt.<\/p>\n<h4><strong>Example: Calculating Leveraged Return<\/strong><\/h4>\n<p>For a $250,000 equity portfolio with an annual 9% total investment return, 40% financed by debt at 6%, the leveraged return would be:<\/p>\n<p>$$R_L=R_P+\\frac{V_B}{V_E}\\left(R_P-r_D\\right)=9\\%+\\frac{$100,000}{$150,000}\\left(9\\%-6\\%\\right)=11\\%$$<\/p>\n<blockquote>\n<h3><strong>Question<\/strong><\/h3>\n<p>A $7,500,000 equity portfolio is 35% financed by debt at a cost of 5% per annum. If the equity portfolio generates a 9% annual total investment return, the leverage return is <em>closest<\/em> to:<\/p>\n<ol type=\"A\">\n<li>8. 25%.<\/li>\n<li>11.15%.<\/li>\n<li>14.00%.<\/li>\n<\/ol>\n<p>The correct answer is <strong>A<\/strong>.<\/p>\n<p>$$\\begin{align}R_L&amp;=R_P+\\frac{V_B}{V_E}\\left(R_P-r_D\\right)\\\\&amp;=9\\%+\\frac{\\$2,625,000}{\\$4,875,000}\\left(9\\%-5\\%\\right)=11.15\\%\\end{align}$$<\/p>\n<\/blockquote>\n\n\n<div style=\"text-align: center; margin: 40px 0;\">\n  <a style=\"display: inline-flex; align-items: center; justify-content: center; padding: 12px 20px; border-radius: 999px; background-color: #1a73e8; color: #ffffff; text-decoration: none; font-weight: 600;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\">\n    Start Free Trial \u2192\n  <\/a>\n  <p style=\"font-size: 15px; margin-top: 12px; color: #555;\">\n    Practice time-weighted, money-weighted, and holding period returns with CFA Level I questions.\n  <\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Other Return Measures Gross and Net Return The gross return is what an asset manager earns before subtracting various costs such as management fees, custody fees, taxes, and other administrative expenses. However, it does account for trading costs such as&#8230;<\/p>\n","protected":false},"author":15,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[2],"tags":[],"class_list":["post-45226","post","type-post","status-publish","format-standard","hentry","category-quantitative-methods","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Other Return Measures - AnalystPrep | CFA\u00ae Exam Study Notes<\/title>\n<meta name=\"description\" content=\"Explore various return measures in finance, including gross and net returns, pre-tax and after-tax nominal returns, and leveraged returns.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/other-return-measures\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Other Return Measures - 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